B. LARGE-SCALE EXAMPLE: COMPUTATIONAL DETAILS
IV. CONCLUSIONS
In this thesis, we have developed two mixed-integer, linear optimization models, PSOM and RSOM, which can guide planners on the resourcing of U.S. Navy submarine maintenance conducted by the tenders in the Fifth and Seventh Fleets. Assuming demand for maintenance tasks is known, PSOM schedules (a) workers to tasks, and (b) personnel travel (as a FAT or by tender), over time. The schedule minimizes penalties for delayed and/or incomplete work, personnel travel, and personnel dwelling with or without a tender. A second model, RSOM, can be used to accommodate emergent, unscheduled demands by producing an updated schedule that minimizes the impact of needed changes on the existing schedule. We have demonstrated these complementary models using a small, fictitious scenario. We have also used a larger, notional scenario to demonstrate the computational feasibility of the approach.
PSOM and RSOM can be improved in several areas, as outlined next:
• Both models should be exercised with real data to validate the approach.
This will allow us to determine key features that need to be modified from or added to the model specifications.
• Penalties for delayed and incomplete work are subjective (i.e., they do not correspond with direct dollar costs). While the flexibility in setting those penalties may allow planners to produce different courses of action, it also lends itself to (possibly unconscious) manipulation to seek an anticipated output. Additional constraints (e.g., limiting the total delayed or incomplete work) could replace subjective penalties.
• Both models can be enhanced by better accounting for precedence relationships among tasks. Currently, neither model has visibility of task precedence except via availability windows: if Task 1 is a predecessor for Task 2, planners must input those windows without overlapping.
However, this prevents feasible options where, for example, if Task 1 is scheduled to be completed early, Task 2 should also be allowed to begin early.
• A final improvement for RSOM is to incorporate decision variables for the movement of submarines with unscheduled demands. The resulting model would determine the optimal location for the maintenance resources and submarines to meet.
More broadly, optimization and simulation can be employed to answer the overarching question about tender and submarine homeports.
Finally, during conversations with planning personnel, it has been pointed out the usefulness of a full job-shop model capability for each of the tenders individually considered. Developing such capability would greatly enhance the current maintenance planning process, which is only aided by Microsoft Project Scheduler [39].
APPENDIX
Below is the full PSOM solution output for Scenario 1, organized by category.
Summary Output
Objective Function Value is 3267.0
Objective Function Breakdown:
Cost of delayed maintenance: 2138.0 Cost of transporting personnel: 285.0
Total cost for personnel at all locations: 788.0
Total savings for personnel collocated with a tender: 659.0 Tender movement costs: 200.0
Total cost for tenders at all locations: 515.0 Cost of unmet maintenance: 0.0
Schedule by day and location
Day Port Task Complete Delayed Number of Workers Allocated by Type
Day 1
GUAM
Task1 8 29 8 Nuclear Task2 8 24 8 Electric Task3 12 31 12 Mechanic DG
Task4 4 27 3 Mechanic 1 Nuclear Task5 4 38 4 Electric
SINGAPORE BAHRAIN
Day 2
GUAM
Task1 8 21 8 Nuclear
GUAM
Task9 7 28 2 Electric 5 Mechanic
BAHRAIN
Task10 7 26 7 Mechanic
SINGAPORE
SINGAPORE
GUAM
BAHRAIN
BAHRAIN
Day 32
GUAM
Task18 6 0 6 Mechanic Task19 2 0 2 Mechanic Task20 9 0 9 Nuclear DG
Task21 6 1 6 Electric Task22 5 0 5 Nuclear SINGAPORE
BAHRAIN
Day 33
GUAM DG
Task21 1 0 1 Electric SINGAPORE
BAHRAIN
Day 34
GUAM DG
SINGAPORE BAHRAIN
Day 35
GUAM DG
SINGAPORE BAHRAIN
Unmet tasks
Travel by worker type and day
Day 13 6 worker(s) waits at GUAM
Day 30 6 worker(s) waits at GUAM
Day 8 5 worker(s) waits at SINGAPORE
Day 23 8 worker(s) waits at DG
Day 4 10 worker(s) waits at GUAM
Day 17 9 worker(s) waits at GUAM
Day 34 9 worker(s) waits at GUAM Day 34 5 worker(s) waits at DG Day 35 9 worker(s) waits at GUAM Day 35 5 worker(s) waits at DG
Tender travel (FCB = USS Frank Cable, ESL = USS Emory S. Land) Day 1 FCB waits at GUAM
Day 19 FCB waits at GUAM
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